1. Field of Invention
The present application is directed towards systems and methods for simulating an environment using multi-staged grids.
2. Description of Related Art
Numerical methods are often used to design and predict a variety of mechanical systems. An example of such a system may include a liquid film between two moving rollers as shown in FIG. 1. This liquid film may be a lubricant or part of a printing process. An interface forms between the liquid film and the ambient environment, such as air. The shape of the interface is of interest to designers of the system. The shape of interface is dependent on the velocity of the rollers, the shape of the rollers, the physical properties of the liquid and the environment.
The designers of the system may simulate the behavior of the fluid by dividing up a simulation space between the rollers with a quadrilateral grid. Prior art methods that have been used to divide up the simulation space have had the same number of cells in the vertical direction throughout the simulation space. As shown in FIG. 1 the opening of the simulation domain is wider than the nip of the simulation domain.
As shown in FIG. 1 while the nip of the simulation space is more than adequately described using 6 cells, the opening and the midpoint of the simulation space is not adequately described using 6 cells. FIG. 2 is an illustration of a simulation space similar to FIG. 1 in which 16 cells are uniformly distributed along the vertical direction. In FIG. 2, the opening and the midpoint of the simulation space are more than adequately described using 16 cells, while an excessive amount of resources are used to describe the nip of the simulation space.
The present invention is a system and method to simulate a simulation space such as the one shown in FIG. 1 while effectively using the computational resources available, and still maintaining the advantages of a quadrilateral grid.